pi-Profiling Concepts Post December 2011 using [ 16/pi ] denoted f1 ( updated August 10th 2018. 7:18 AM. )

.

Author: Kevin John Trinder, independent researcher .

Please note i am dyslexic and use of the periods is to keep me focused .

We began this paper on October 30th 2013. update have fallen behind due to illness . .

Introduction: Mathematical Poem on Circle: Plane Figure ( circle ) PFC .

Circle: Definition of plane-figure circle ( PFC ) and its circumference ( cir ) .

In Geometry all lines and all points have no width, breadth or depth .

Our PFC’s circumference when drawn on a perfectly flat plane, is an imaginary perfect curve of infinitely many imaginary points .

being of no width, breadth or depth . .

Our PFC’s centre is also an imaginary point being of no width, breadth or depth . .

Each of the infinitely many imaginary points of our PFC’s circumference is equidistant from our PFC’s imaginary centre point . .

Lines may be drawn tangent to our PFC’s circumference but not reside on our PFC’s circumference . .

The surface area within our PFC does not encroach onto our PFC’s circumference . .

At no time should we imply that numerical concepts or numerical outcomes reside on the circumference of our PFC . .

When we assign a numerical value in general to our PFC’s diameter D we change the dynamics of our PFC's perfectly .

curved circumference to a pi-Profiling Perimeter ( P ) .

pi dose not reside on our PFC’s circumference, it is a pi-Profiling Perimeter P value, residing just below our PFC's circumference . .

The agreed and accepted value of pi extracted from prime numbers is a truncated constant meaning that there is a time lapse from .

observing the largest known prime number to the next yet to be found progressive largest prime number . .

When the diameter D of our pi-Profiling Perimeter P is positive integer one our pi-Profiling Perimeter P is pi . .

When the diameter D of our pi-Profiling Perimeter P is the inverse of pi our .

pi-Profiling Perimeter P is [ pi * (1/pi) ] is notionally positive integer one . .

When we consider the diameter of our PFC to be a straight line of infinitely many imaginary points being of no width, breadth or .

depth we can use our pair of compasses and unmarked rule to show the imaginary point along our diameter D for .

our Golden Section Ratio ( GSR ) . .

From our pi-Profiling Perimeters P diameter D and radius R we can give our GSR value from right angle triangle D : R and the first .

and second cuts with our pair of compasses . .

Kevin John Trinder, began October 30th 2013. updated May 26, 2016.

Page ! of !1 25

Abstract .

To find the word seeds of notion to describe the numerical environment within and about our .

pi-Profiling Perimeter P observed when we assign a numerical value in general to .

our Plane Figure ( circles ) diameter using an electronic spreadsheet or computer program . .

We begin . .

pi-Profiling Formula Facilitators ( f ) are denoted { f1, f2, f3, f4, f5, f6 . . . } .

pi-Profiling Environment Formula Facilitators ( e ) are denoted { e1, e2, e3, e4, e5, e6, e7 . . . } . .

Known Formula Facilitators ( KF ) are agreed and accepted Number Theory constants and Mensuration aid values .

for example: pi itself and our Golden Section Ratio ( GSR ), the sqrt 2, the sqrt 3, the sqrt 5, the sqrt 6 . .

From about 1989, my dyslexic mind began thinking about and asking, why its it that when we .

divide a numerical outcome in general by pi that the quotient may considered notionally to be .

the radius R squared R^2 of our pi-Profiling Perimeter P ? .

Not so long after the above question came to mind, i was thinking about dividing the square root .

of all sorts of numerical outcomes and VOI, into our pi-Profiling Perimeter P .

The day arrived when i divided the square root of 2/4, 0.5, into our pi-Profiling Perimeters 1P value .

of 2pi, giving us the quotient of 8.88576587631673 denoted 1Psi

1Psi being the number of √D/4 increments about our pi-Profiling Perimeter 1P . .

for a pi declaration of 3.14159265358979 denoted pi14, being pi to14 decimal places .

1Psi =~ ( 2pi ) / ( √0.5 ) =~ 8.88576587631673 =~ 1Psi .

i was to find out later that 8.88576587631673 divided by two being 4.44288293815837 was a Geometric Mensuration Aid Value . .

it was not long before i realised that many of the electronic spread sheet outcomes i was observing .

were close numerical outcomes found in many Scientific Papers on all sorts of Scientific topics. .

From about 1989 onwards my electronic spreadsheet input values for entering the numerical .

environment within and about our pi-Profiling Perimeter 1P, was via its diameter 1PD . .

It was not until January 2012 that i began to observe strange interconnecting data values that were .

not changing on my electronic spreadsheet when the input diameter 1PD value was varied .

i began to observe what i called then, square root of x, (SOX) formulas, (SOXf’s) . .

My first observed pi-Profiling Formula Facilitator ( f ) was 8.88576587631673 and today denoted as f108 .

Page ! of !2 25

January 2012, i also observed that [ (pi/3) * (√1.125) ] =~ 1.11072073453959 denoted as f101 . .

f1 is (16/pi ) =~ 5.09295817894065 .

f2 is 8*( √pi ) =~ 14.1796308072441 .

f3 is [ ( pi )^2 ] / ( f2 ) / 4 ] =~ 2.78416399841585 .

f4 is 4pi =~ 12.5663706143592 .

f5 is 1/pi =~ 0.318309886183791 .

f6 is √pi =~ 1.77245385090552 .

f7 is pi/3 =~ 1.047197551196 .

f8 is √ (4/pi ) =~ 1.12837916709551 or 2 / f6 .

f9 is (1/4pi) =~ 0.079577471545947 .

f11 is 2pi =~ 6.28318530717959 .

f12 is (4/pi ), being 1.27323954473516. or ( f8 )^2 or ( 2 / f6 )^2 .

f13 is [ (pi/2) -1 ] =~ 0.570796326794897 .

f14 is ( [ f180 being 1.37596919694205. ] / f12 ) =~ 1.08068368016975 .

f15 is ( [ f181 being 2.7519383938841. ] / f12 ) =~ 2.1613673603395 .

f16 is (2pi)^2 =~ 39.4784176043574 .

f17 is f16 / f6 =~ 22.2733119873268 . .

My next pi-Profiling observations were, what i call today August 4th 2018, .

pi-Profiling Environment Formula Facilitators ( e) .

observed when we are pi-Profiling via the diameter 1PD of our pi-Profiling Perimeter 1P .

these e values are observed when we divided our diameter 1PD being our VOI input value by .

our f1 value, the quotient being our pi-Profiling Environment Formula Facilitator value, denoted e1 .

e values are denoted { e1, e2, e3, e4, e5, e6 . . . } .

pi-Profiling Formulas e1, e2, e3, e4, e5 .

[diameter D] / (f1) gives us e1 n.b. our P value divided by 16 also gives us e1 .

the √(e1) gives us e2 .

the √(e2) gives us e3

.

(e1) * (e2) gives us e4 .

(e1) * 2 gives us e5 .

When our value of interest VOI and our diameter 1PD input value is the Known Facilitator ( KF ) .

Page ! of !3 25

value for the Golden Section Ratio being 1.61803398874989 .

our e value outcomes are as follows .

1.61803398874989 1PD diameter and our value of interest ( VOI ) and our input value

5.09295817894065 f1 quotient =~ 0.317700230769704 1Pe1 being 1PD/(f1) .

0.317700230769704 1Pe1 being 1PD/(f1) square root =~ 0.563649031552174 1Pe2 being the √(1Pe1) .

0.563649031552174 1Pe2 being the √(1Pe1) square root =~ 0.750765630241671 1Pe3 being the √(1Pe2) or √[√(1Pe1)] .

0.317700230769704 1Pe1 being 1PD / (f1) 0.563649031552174 1Pe2 being the √(1Pe1) product =~ 0.179071427397246 1Pe4 being (1Pe1) * (1Pe2) .

0.317700230769704 1Pe1 being 1PD / (f1) 2 product =~ 0.635400461539407 1Pe5 being (e1) * 2

We will use e1 through e5 for pi-Profiling of our VOI and D value 1.61803398874989 .

n.b. our pi-profiling data output here only gives consideration to pi-Profiling Perimeter 1P its .

diameter 1PD, its (1PD)*2, its radius 1PR, its (1PD)/4 denoted Di, its area 1PA, its number of √(Di) increments Psi .

and companion values ( c ) for each of the above, its companion Sphere surface area Ssa .

its companion Sphere Volume SV and we begin to consider our pi-Profiling Formula ( pPF ) .

and its pi-Profiling Formula Facilitator ( f ) for the inverse of diameter D. .

n.b. There are many, many other facets of Geometry not considered at this time . .

pi-Profiling Environment Facilitator Formulas ( e ) outcomes for our VOI and .

diameter 1PD input value of 1.61803398874989 being our Golden Section Ratio ( GSR ) . .

1.61803398874989 1PD our pi-Profiling Perimeters diameter and VOI being our ( GSR ) . 5.08320369231526 1P pi-Profiling Perimeter 1P . 0.809016994374947 1PR radius R . 0.654508497187473 1PR^2

. 0.654508497187473 1PR^2

0.317700230769704 1Pe1 quotient =~ 2.06014485920194 (1PRc)^2 our companion radius value to 1PR^2 .

2.05619908647626 1PA our pi-Profiling Perimeters area 1PA

0.317700230769704 1Pe1 quotient =~ 6.47213595499958 1PAc our companion area value to area 1PA . n.b. 1PDi * 16 =~ 1PAc .

Page ! of !4 25

. 8.22479634590505 Ssa surface area of our pi-Profiling Perimeters companion Sphere 1PSa

0.317700230769704 1Pe1 quotient =~ 25.8885438199983 Ssac companion sphere surface area value to 1PSsa .

1.61803398874989 1PD our pi-Profiling Perimeters diameter and VOI being our GSR 0.563649031552174 1Pe2 quotient =~ 2.87064094529562 1PDc our companion diameter value to 1PD . 0.809016994374947 1PR our radius 1PR 0.563649031552174 e2 quotient =~ 1.43532047264781 1PRc our companion radius value to 1PR .

5.08320369231526 1P our pi-Profiling Perimeter denoted P 0.563649031552174 1Pe2 quotient =~ 9.01838450483478 1Pc our companion perimeter for our pi-Profiling 1P .

0.404508497187474 1PDi our pi-Profiling Perimeters D/4 value, denoted 1PDi 0.563649031552174 1Pe2 quotient =~ 0.717660236323905 1PDe our companion D/4 value to 1PDi .

0.636009824757034 √(1PDi) 0.750765630241671 1Pe3 quotient =~ 0.847148296536035 √(1PDe) our companion square root value to √(1PDi) .

7.99233517227052 1Psi, number of √(Di) increments (s) about our pi-Profiling Perimeter 1P 0.750765630241671 1Pe3 quotient =~ 10.6455794595949 1Psic number of √(1PDe) increments about 1Pc .

2.21800000637005 SV volume of our our pi-Profiling Perimeters companion Sphere 1P 0.179071427397246 1Pe4 quotient =~

12.3861189839612 kSV our companion sphere volume value to 1PSV .

3.23606797749979 ( D*2 ) our pi-Profiling Perimeters diameter 1PD times two 0.635400461539407 1Pe5 product =~ 2.05619908647626 1PA our pi-Profiling Perimeters area 1PA .

2.05619908647626 1PA our pi-Profiling Perimeters area 1PA 0.317700230769704 1Pe1 quotient =~ 6.47213595499958 1PAc our companion area value to area 1PA

As we add more facets of geometry to our electronic spreadsheet our pi-Profiling data becomes more interesting .

Authors note: March 22, 2016. ( updated April 6th 2016. PM ) .

Science and the notion of 1.37596919694205 inverse value being 0.7267604552648 .

i have noticed recently that you are using Quote: 2-(4/pi) =~ 0.726760455264. End-quote .

and Quote: 1-(2/pi) =~ 0.36338022763242 End-quote .

Page ! of !5 25

OK, lets consider the notion of one Radian and our pi-Profiling Perimeters numerical environment . .

The following internet searches may not be related: Physics, Particle Physics, Nuclear Physics .

notion of quantum random walks or perhaps you are considering EPR Paradox – Bell’s Inequality .

Perimeter logic or the notion of electronics and the numerical outcome of 0.726760455264837 .

inverse value being 1.37596919694205 or Kepler’s Equation’s and the notion of .

Quote: calculate the true anomaly . . . =~ 1.3759 End-quote. .

or Newtonian Dynamics or Solar Energy Fundamentals and 2.1613673603395 or the .

Control Rod Insertion Problem, Quote: Table 1, position 1, MPpard, 1.37597 End-quote .

or Quote: The maximum event time for KM3NeT is 8300 ns End-quote

.

.

pi-Profiling Formulas for one Radian: .

On September 13, 2014, i posted the following area A pi-Profiling Formula to the internet .

n - [{[{√n}/2]2}*pi] =~ [{[{√n}/2]2}*pi] - { [{[{√n}/2]2}*pi] / 1.37596919694205} .

where n =~ diameter D squared, n =~ D^2 or √n =~ D .

inverse of 1.37596919694205 is 0.72676045526484 .

1.37596919694205 is my pi-Profiling Formula Facilitator f180 .

n.b. 180 refers to one Radian being 57.2957795130822 .

pi-Profiling Formula for f180 .

f180 =~ 1.37596919694205. =~ [(D^2) / ( f12 )] / [(D^2) / ( f13 )] .

pi-Profiling Formula for f181 .

f181 =~ [ f180 * 2 ] =~ 2.7519383938841 . .

pi-Profiling Formulas for one Radian: .

[ 90 / { [{[(D^2) / ( f12 )] / f180} / 8] / [{D}/2]^2}/2] } ] / f181 =~ 57.2957795130822 =~ 1 Radian .

summarised as: [ 90 / f13 ] / f181 =~ 57.2957795130822 =~ 1 Radian .

example for n =~ 31 =~ D^2 =~ (5.56776436283002)^2 =~ 31 . .

example for n = 31 =~ D^2 =~ (5.56776436283002.)^2 =~ 31 .

5.56776436283002 our pi-Profiling Perimeters diameter D and √n .

31 n, being D^2, (5.56776436283002)^2 1.27323954473516 f12 quotient =~ 24.3473430653209 area 1PA, [(1PD^2) / ( f12 )] .

Page ! of !6 25

24.3473430653209 area 1PA, [(1PD^2) / ( f12 )] 1.37596919694205 f180 quotient =~ 17.6946861306419 {[(1PD^2) / ( f12 )] / f180} .

17.694686130641 {[(D^2) / ( f12 )] / f180} 8 positive integer 8 quotient =~ 2.21183576633024 [{[(D^2) / ( f12 )] / f180} / 8] .

2.21183576633024 [{[(D^2) / ( f12 )] / f180} / 8] 3.875 [{[{D}/2]^2}/2] or ( n / 8) quotient =~ 0.5707963267949 f13 , being ( pi/2 ) -1 .

.

90 positive integer 90 0.5707963267949 f13 quotient =~ 157.67445544957 90/f13 .

157.67445544957 90/f13 2.7519383938841 f181 , being [ (f180) * 2 ] quotient =~ 57.2957795130822

n.b. f14 is ( [ f180 / f12 ] =~ 1.08068368016975 .

n.b. f15 is f181 / f12 ) =~ 2.1613673603395 .

Authors note: April 1, 2016. Quote: Keywords, KM3NeT; Neutrino telescope; Trigger End-quote Quote: The maximum event time for KM3NeT is 8300 ns End-quote

.

. we observe 57.2957795130822 * 10 =~ 572.957795130822. being ( 1Psi ) .

we observe [(572.957795130822 / 4pi)^2] *4 =~ 8315.44562629427 being our diameter 1PD .

? we may be observing a base10 anomaly ? . .

Authors notes: April 3, 2016. ( updated June 6, 2016 ) .

OK, lets consider the notion of our pi-Profiling Perimeters P and the inverse of its diameter 1PD. .

My pi-Profiling Formula for the inverse of our diameter, 1/1PD is: .

1/PD =~ f16 / (Psi)^2 . .

where f16 is (2pi)^2 being 39.4784176043574 .

Kevin John Trinder, April 3, 2016.

.

.

Page ! of !7 25

Authors notes: February 14th 2016. ( updated April 7, 2016 PM) .

We have observed that approximation inverse values for our notional fine-structure ( α ) outcomes are found .

between 1Psi =~ 73.5427 and Ps =~ 73.553 via pi-Profiling Formula [( Ps / 4pi )^2] * 4 =~ approx. 1 / α

.

.

Authors note: February 18th 2016. updated August 2018. . .

When we use the number six, or we have six of anything . >< .

or when we use √2, √3 and √6 we must be aware that 4 * ( √ pi ) being 7.0898154036221

may be written as: {(√pi/3)*(√8)}* [√6] =~ 4*√pi . 1.02332670794649 being √ ( pi / 3 ) 2.82842712474619 √8 product =~ 2.89440501823307 being [ √ ( pi / 3 ] * [ √8 ] .

2.89440501823307 being [ √ ( pi / 3 ] * [ √8 ] 2.44948974278318 being √6 also being (√2) * (√3) product =~ 7.08981540362206 being 4 * ( √ pi )

my concern is in reference to the notion of Hadrons, Mesons ( 1 quark plus 1 anti-quark ) and the quotients arrived at by division using √2 ,√3 and √6

.

Authors notes: February 20th 2016.

when we use number six, or we have six of anything containing .

or dividing by number 6 .

. >< .

6, √6, (1/pi) and the notion of Quote: C-parameter and coupling constant End-quote . .

Authors notes: February 20th 2016.

Quote: Particle momentum in the Centre of Mass

Quoting paper: Properties of C-parameters and coupling constant

Contributions to C-parameter n=~2; A; 2.4317 End-quote. . .

Ok, i am know going back to October 29th 2002 when i observed the following pi-Profiling outcome of : 2.43170840741611 .

i posted the pi-Profiling Formula for this outcome 2.43170840741611. to my web site at that time. . .

pi-Profiling Formula for 2.43170840741611:

Page ! of !8 25

pi-Profiling Formula for 2.43170840741611: . 2.44948974278318 √6 0.318309886183791 1/pi denoted f5 product =~ 0.779696801233676 ( √6 ) * ( 1/pi ) 0.779696801233676 ( √6 ) * ( 1/pi ) squared =~ 0.607927101854027 [ ( √6 ) * ( 1/pi ) ]^2 . 0.607927101854027 [ ( √6 ) * ( 1/pi ) ]^2 4 product =~ 2.43170840741611 pi-Profiling Formula outcome for 2.43170840741611

Authors notes: February 23rd 2016.

Our Notional Value for the Speed of Light Cn may be written many ways: .

n.b. pi-Profiling outcomes observed within and about the numerical environment of our .

pi-Profiling Perimeter P, do not imply units or status, we do that .

pi-Profiling Formula for Notional Value for the Speed of Light Cn

Cn =~ sqrt [{( 5/sqrt pi ) * 10^17} / pi] =~ 299,655,737.5766 .

Cn =~ sqrt [{ [2pi / sqrt (pi^3) ] * 10^18} / 4pi ] =~ 299,655,737.5766

Cn =~ sqrt [ { [ sqrt ( 4/pi ) ] * 10^18 } / 4pi ] =~ 299,655,737.5766

Kevin John Trinder, February 23, 2016.

.

.

Page ! of !9 25

Authors notes: January 30th 2016. ( updated April 6, 2016 ) . .

Introducing wDi . .

What is the purpose for wDi ? .

wDi =~ ( 1Psi / 4pi ) where 1Ps is a nominated positive or negative number in general

Our nominated 1Psi value times our wDi value, equals our pi-Profiling Perimeter 1P, 1Psi * wDi =~ 1P

Our pi-Profiling Formula for our perimeters P diameter 1PD is: [ ( wDi )^2 ] * 4 .

When 1Psi equals pi we are saying that our wDi value =~ ( pi/4pi ) .

we are saying that ( pi / 4pi ) =~ wDi =~ 0.25 .

and ( 0.25 )^2 =~ 0.625 =~ our diameter 1PD/4

and

(0.625) *4 =~ our diameter 1PD =~ 0.25 .

and ( 0.25 * pi ) is our pi-Profiling Perimeter 1P =~ 0.785398163397448 .

being ( Ps * wDi ) .

Using wDi gives us a progressive work-around companion square root value for .

our 1P diameter on 4, 1PD/4 .

. In other words, when we are pi-Profiling and

. we use a nominated positive or negative number in general for

. our electronic spreadsheets 1Ps input value

. by doing so we are

. driving or controlling the numerical environment within and about pi-Profiling Perimeter 1P

.

.

Introduction

Authors notes: February 1, PM, 2016. ( updated April 7, 2016 ) . .

Exhaustion about our Plane Figure ( circle ) circumference

.

. Our concept of the companion square root of x ( csqrtx ) now denoted wDi

was observed prior to June 7th 1996. with no word seeds of notion to describe our wDi concept:

Observing wDi as being the square root of 0.5 we observed

our value for 1Psi as [ f101 *8 ]

.

.

Page ! of !10 25

Authors notes: January 24th 2016. ( updated March 9, 2016 ) . .

Since observing the numerical outcomes of our square root of x ( SOFX ) formulas ( SOXf ) .

and pi-Profiling Formula Facilitators ( f ) in January 2012 .

i have spent the last four years .

pi-Profiling the numerical environment of our pi-Profiling Perimeter P .

looking for the word seeds of notion .

to describe our concept of the companion square root of x ( csqrtx ) . .

We observed the pi-Profiling Formula for the csqrtx now denoted wDi as: .

for positive and negative numerical values in general ( n ), wDi =~ 1Psi / 4pi .

our Psi value, is the number of wDi increments about our pi-Profiling Perimeter 1P .

n.b. 4pi =~ 12.566370614359 and is our pi-Profiling Formula Facilitator denoted f4 .

Our radical sign will be replaced with the symbol wDi .

Authors notes: December 21st 2015 ( updated August 2018 )

Abstract

To give a pi-Profiling Loop Formula observed from wDi

allowing us to observe our Notional Electroweak Mixing Angle

Our pi-Profiling input value will be our 1Psi value, which is our VOI

.

. n.b. wDi denotes my notion of the companion square root of x and work-around for 1Pe2

.

.

n.b. To observe our value of interest being the Notional Electroweak Mixing Angle .

our pi-Profiling input value at 1Psi will be positive integer and prime number 13 . .

n.b. our 1Psi value, is the number of wDi increments about our pi-Profiling Perimeter 1P . .

n.b. our 1PD/4 value is denoted as 1PDi and 1PDi has a companion 1PD/4 value denoted 1PDe .

n.b. our pi-Profiling Formula for wDi is: wDi =~ [ Psi / 4pi ] .

and [ wDi ]^2 =~ D/4 .

n.b. wDi has a companion value denoted wDe . .

n.b. Because we are pi-Profiling the numerical environment within and about our 1P .

via our 1Psi value, we need to be able to identify the status of observed numerical outcomes .

so we will underscore the status of our observed numerical outcomes, for example: .

our pi-Profiling Perimeter 1P and its diameter 1PD will be underscored, 1P and 1PD . .

our companion pi-Profiling Perimeter 1Pc and diameter 1PDc will be underscored, 1Pc and 1PDc .

Page ! of !11 25

. n.b. for our e values that have been identified for 1Psi will have there alphabetical tags

.

will be underscored also, for example: 1Pe1 , 1Pe2 , 1Pe3 , 1Pe4 ,1P e5 . .

Notional pi-Profiling Formula for Electroweak Mixing Angle . .

First we observe our pi-Profiling Formula for our Notional Electroweak Mixing Angle

by declaring our pi-Profiling Formula Facilitator ( f ) denoted f3

Notional pi-Profiling Formula for Electroweak Mixing Angle . 9.86960440108936 pi^2 3.54490770181103 {[(f6)*4]/2}, where f6 is the square root of pi =~ 1.77245385090552 quotient =~ 2.78416399841585 f3 facilitating our 1PDc value, 1PDc =~ ( 1Psi / 2.78416399841585 )

.

13 1Psi and number (n) of wDi increments about our pi-Profiling Perimeter 1P 2.78416399841585 f3 being [ (pi)^2 ] / ( f2 ) / 4 ] quotient =~ 4.66926517525433 1PDc our companion value to 1PD 1.03450713009732 wDi, wDi is: wDi =~ (Ps /4pi) n.b. 4pi is our f value denoted f4 sum squared =~ 1.07020500222219 ( wDi )^2 and our perimeters ( 1PD / 4) denoted 1PDi .

1.07020500222219 ( wDi )^2 and our perimeters ( 1PD / 4) denoted 1PDi 4 product =~ 4.28082000888877 gives us our perimeters diameter 1PD .

4.28082000888877 our perimeters diameter 1PD inverse =~ 0.233600104167795 our Notional Electroweak Mixing Angle being observed from wDi

.

.

My pi-Profiling Formula for the inverse of diameter 1PD, (1/1PD)

1/1PD =~ f16 / (1Psi)^2

. 39.4784176043574 f16 is (2pi)^2 being 39.4784176043574 169 ( 1Psi )^2 where 1Psi =~ 13 quotient =~ 0.233600104167795 our Notional Electroweak Mixing Angle being observed from wDi inverse =~ 4.28082000888877 our pi-Profiling Perimeters diameter D

.

.

Authors notes: by-passing the Square Root Function for e2 . 4.28082000888877 1PD our pi-Profiling Perimeters diameter 1PD 4.66926517525433 1PDc our companion diameter value to 1PD quotient =~ 0.916808073265103 being e2, our pi-Profiling Environment Formula Facilitators e2

n.b. Using Psi as our input value for pi-Profiling, allows us to observe our .

work-around value for 1Pe2 0.916808073265103 our 1Pe2 sum squared =~ 0.840537043204071 our 1Pe1

Page ! of !12 25

.

0.840537043204071 our 1Pe1 5.09295817894065 our f1 product =~ 4.28082000888877 1PD our pi-Profiling Perimeters diameter 1PD

.

4.28082000888877 1PD our pi-Profiling Perimeters diameter 1PD pi 3.14159265358979. product =~ 13.4485926912652 our pi-Profiling Perimeter 1P being [ wDi * 13 ]

.

.

Authors notes: December 21st 2015. ( updated August 5th 2018 ): .

Since January 2012. i have not been able to breach 1PDc : 1Pe2 and i am .

confident to breach 1PDc : 1Pe2 ( the impassable bridge ) would be improbable

.

.

When Ps =~ 13 . wDi =~ 1.03450713009732. =~ ( 13 / 4*pi ) . ( wDi )^2 =~ 1.0702050022221 =~ our perimeters diameter 1PD on 4, ( 1PD / 4 ) value. . .

We observe 4*pi =~ 12.566370614359. =~ f4 . when Psi =~ 12.566370614359. we observe wDi =~ 1 and 1^2 =~ 1, our 1PDi value . when Psi =~ -12.566370614359. we observe wDi =~ -1 and -1^2 =~ 1, our 1PDi value . We can observe wDi as ( -pi / pi ) =~ -1 and (-1)^2 =~ 1 . .

When 1Psi =~ 1 we observe wDi =~ 1/4pi =~ 0.0795774715459 and (1/4pi)^2 =~ 0.0063325739776 our 1PDi value .

When 1Psi =~ -1, we observe wDi =~ -0.079577471545947 and ( -0.079577471545947 )^2 =~ 0.006332573977646 our 1PDi value

.

n.b. We observe that for 1Psi =~ 1 and for 1Ps =~ -1 our perimeter P and its wDi value .

are equal to each other being 0.079577471545947 =~ 1/4pi being f9 .

We observe pi/3 =~ 1.047197551196 =~ f7 . when 1Psi =~ -12 we observe wDi =~ -0.95492965855137 =~ 1/( -1.047197551196 ) . we observe -0.95492965855137^2 =~ 0.91189065278104 =~ ( 9 / pi^2 ) .

we observe -0.95492965855137 / 0.91189065278104 =~ pi/3 =~ 1.047197551196 . when 1Psi =~ -1.047197551196 we observe wDi =~ -0.08333333333333 =~ 1/-12 . we observe -0.08333333333333^2 =~ 0.006944444444444 =~ our perimeters 1PD/4. .

we observe 0.0069444444444444 * 4 =~ 1/36

. we observe 0.0833333333333333 =~ 1/12

Page ! of !13 25

We observe pi divided by the square root of 8 =~ 1.110720734539 =~ f101 . when 1Psi =~ ( f101 ) we observe wDi =~ 0.0883883476483 . we observe 0.0883883476483^2 =~ 0.0078125 =~ our 1PDi value

. we observe pi divided by 3 =~ 1.047197551196 =~ f7 . we observe the square root of 1.125 =~ 1.0606601717798 . we observe (f101) / (f7) =~ 1.0606601717798 being f109 ( observed January 2012 )

.

When 1Psi =~ {1, 2, 3, 4, 5, 6…} . we observe wDi =~ 1* (1/4pi), 2* (1/4pi), 3* (1/4pi), 4* (1/4pi), 5* (1/4pi), 6* (1/4pi), … . we observe: f9 being 1/4pi =~ 0.079577471545947 . and 0.079577471545947 * 10 =~ [1*(1/4pi)] + [2*(1/4pi)] + [3*(1/4pi)] + [4*(1/4pi)]

.

.

When 1Psi =~ GT 2015 November 23rd =~ 6.6743257318364124595179244522346e-11 . we observe wDi =~ 0.53112596601359 . [( 0.53112596601359. )^2] * 4 =~ 2/( f6 ) =~ 1.12837916709551 being f8 and ( f8 )^2 =~ 4/pi .

1/{[(0.53112596601359)^2]*2} =~ the square root of pi =~ 1.7724538509 being f6 . .

GT 2015 November 19th = 6.6743257318364124595179244522346e-11

https://pi-profiling.info/abstract_documents/2015_nov_19-pi-profiling_formula_2015_for_notional_gravitational_constant_using_golden_ratio.pdf

.

.

GT 2015 November 23rd =~ 6.6743257318364124595179244522346e-11

https://pi-profiling.info/abstract_documents/2015_nov_23_pi-profiling_formula_2015_for_notional_gravitational_constant_using_golden_ratio.pdf

.

.

Notional Universal Gravitational Constant 6.6743257318364124595179244522294e-11 .

for a pi declaration of 3.1415926535897932384626433832795

1.7724538509055160272981674833411 sqrt pi inverse =~ 0.56418958354775628694807945156077 1 / ( sqrt pi ) .

0.56418958354775628694807945156077 1 / ( sqrt pi ) 2 positive integer 2 quotient =~ 0.28209479177387814347403972578039 [ 1 / ( sqrt pi ) ] / 2 .

0.28209479177387814347403972578039 ( [ 1 / ( sqrt pi ) ] / 2 ) sqrt =~ 0.53112596601359845723853652425376 sqrt ( [ 1 / ( sqrt pi ) ] / 2 ) .

0.53112596601359845723853652425376 sqrt ( [ 1 / ( sqrt pi ) ] / 2 ) 12.566370614359172953850573533118 f9 being 4*pi product =~ 6.6743257318364124595179244522294 [ sqrt ( [ 1 / ( sqrt pi ) ] / 2 ) ] * 4pi

Page ! of !14 25

On January 16th 2015 i wrote an Elegant pi-Profiling Loop Formula number one (EpPLF1) .

enabling us to observe our numerical outcomes of 55?????? with respect to the .

notion of our fine-structure constant. e.g. prime number 73 FSD 55?????? . .

73 FSD 5524602095245869 ( FSD: full stop delimiter ) .

73.5524602095245869 1Psi number of wDi increments about our pi-Profiling Perimeters 1P 0.0795774715459477 f9 being (1/4pi) product =~ 5.853118809457890857 being our wDi value . 5.853118809457890857 being our wDi value squared =~ 34.25899979762975765 our pi-Profiling Perimeters 1PD/4 value denoted 1PDi .

34.25899979762975765 our pi-Profiling Perimeters 1D/4 value denoted 1PDi 4 product =~ 137.035999190519030630593328668 our pi-Profiling Perimeters diameter 1PD .

137.035999190519030630593328668 inverse of my fine-structure constant value inverse =~ 0.0072973525636115183384116343457 being my notional value for the fine-structure constant:

.

.

Today is January 28th 2016. ( updated April 6, 2016 ) Numerical outcomes .

observed from pi-Profiling when our 1Psi value of interest ( VOI ) is positive integer 13 . .

pi-Profiling the numerical environment within and about our pi-Profiling Perimeter P when our 1Psi value, being the number of wDi increments about 1P

is positive integer 13 . 13 1Psi number (#) of wDi increments about our pi-Profiling Perimeters 1P 2.78416399841585 f3 being [ (pi)^2 ] / ( f2 ) / 4 ] quotient =~ 4.66926517525433 1Dc our companion value to 1PD . 1.03450713009732 wDi wDi =~ 1Ps / 4pi sum squared =~ 1.07020500222219 [wDi]^2 and our pi-Profiling Perimeters 1PD on 4, 1PD / 4 .

1.07020500222219 [wDi]^2 and our pi-Profiling Perimeters 1PD on 4, 1PD / 4 4 product =~ 4.28082000888877 1PD .

4.28082000888877 1PD inverse =~

0.233600104167795 being our Notional Electroweak Mixing Angle observed from wDi . .

4.28082000888877 1PD 4.66926517525433 1PDc our companion diameter value to 1PD quotient =~ 0.916808073265103 being our pi-Profiling Formula Facilitator 1Pe2 .

0.916808073265103 1Pe2 sum squared =~ 0.840537043204071 1Pe1

Page ! of !15 25

0.840537043204071 1Pe1 5.09295817894065 f1 product =~ 4.28082000888877 1PD .

4.28082000888877 1PD 2 quotient =~ 2.14041000444439 1PR radius 1PR .

2.14041000444439 1PR radius 1PR 0.916808073265103 1Pe2 quotient =~ 2.33463258762717 1PRc our companion radius value to 1PR .

4.28082000888877 1PD 4 quotient =~ 1.07020500222219 1PDi being our pi-Profiling Perimeters diameter 1PD on 4, 1PD/4 .

1.07020500222219 1PDi being our pi-Profiling Perimeters diameter 1PD on 4, D/4 0.916808073265103 1Pe2 quotient =~ 1.16731629381358 1PDe our companion value to 1PDi .

4.28082000888877 1PD pi pi to 14 decimal places: pi14, rounding may be occurring product =~ 13.4485926912652 1P our pi-Profiling Perimeter 1P being [ wDi * 13 ] .

13.4485926912652 P our pi-Profiling Perimeter 1P being [ wDi * 13 ] 0.916808073265103 1Pe2 quotient =~ 14.6689291722417 1Pc our companion perimeter value to 1P .

14.6689291722417 1Pc our companion perimeter value to 1P 1.12837916709551 being the square root of 4/pi quotient =~ 13 1Psi number (#) of wDi increments about pi-Profiling Perimeter 1P .

5.09295817894065 f1 0.916808073265103 1Pe2 product=~ 4.66926517525433 1PDc our companion diameter value to 1PD .

1.03450713009732 wDi our pi-PF for wDi is: wDi =~ Ps / 4pi 0.957500952096187 1Pe3 quotient =~ 1.08042412681946 wDe our companion value to wDi

0.840537043204072 1Pe1 16 positive integer 16 product =~

13.4485926912652 P our pi-Profiling Perimeter being [wDi * 13] 1.07020500222219 ( wDi )^2 our diameter 1PD on 4, 1PD / 4 denoted 1PDi 2 product =~ 2.14041000444439 1PR radius 1PR .

4.58135498712562 1PR^2 radius 1PR squared 0.840537043204072 1Pe1 quotient =~

5.45050931921072. (1PRc)^2 our companion radius squared to 1PR^2 Page ! of !16 25

. 8.56164001777754 twice our diameter 1PD, ( 1PD*2 ) 1.68107408640814 1Pe5 product =~ 14.3927511710408 1PA our perimeters area 1PA .

57.5710046841632 1PSsa, our pi-Profiling Perimeters companion Spheres surface area 4 quotient =~ 14.3927511710408 1PA our perimeters area 1PA

14.3927511710408 1PA our perimeters area 1PA 0.840537043204072 1Pe1 quotient =~ 17.1232800355551 Ac our companion area value to 1PA .

1.07020500222219 1PDi being our perimeters diameter 1PD on 4, 1PD/4 16 product =~ 17.1232800355551 1PAc our companion area value to area 1PA . . 14.3927511710408 1PA our perimeters area A 4 product =~ 57.5710046841632 1PSsa our pi-Profiling Perimeters companion Spheres surface area .

4.58135498712562 1PR^2 radius 1PR squared 12.5663706143592 f4 product =~ 57.5710046841632 1PSsa our pi-Profiling Perimeters companion Spheres surface area .

57.5710046841632 1PSsa our pi-Profiling Perimeters companion Spheres surface area 0.840537043204072 1Pe1 quotient =~ 68.4931201422203 1PSsac our companion value to 1PSsa .

4.28082000888877 1PD 16 product =~ 68.4931201422203 1PSsac our companion value to 1PSsa .

4.66926517525433 1PDc our companion value to D squared =~

21.8020372768429 1P(Dc)^2 .

21.8020372768429 1P(Dc)^2 pi product =~ 68.4931201422203 1PSsac our companion value to 1PSsa .

4.66926517525433 1PDc our companion value to 1PD to power of 3 =~ 101.799493406359 1P(Dc)^3

.

101.799493406359 1P(Dc)^3 pi product =~ 319.81254062458 1P[(Dc)^3] * pi .

319.81254062458 1P[(Dc)^3] * pi 6 quotient =~ 53.3020901040967 1PSVc companion volume to our pi-profiling Perimeters companion Spheres volume 1PSV

Page ! of !17 25

53.3020901040967 1PSVc 0.770611147087873 1Pe4 product =~ 41.0751847972992 SV our pi-profiling Perimeters companion Spheres volume 1PSV

.

.

n.b. You may use, copy or store these pi-Profiling Formulas, f, and e formulas their variations and pi-pProfiling Concepts

for educational purposes with attribution to me where possible . .

n.b. In Geometry when we draw a Plane Figure ( circle ) PFC, one leg of our pair of compasses is at .

its centre and the other is scribing its circumference. Having drawn a PFC, its matching pair of compasses .

will not walk evenly around our PFC’s perfectly curved circumference, there will always be a remaining portion . .

Reference ( earlier attempts at writing up pi-Profiling observations )

The following paper requires daily updating as i search for the word seed of notion to describe .

pi-Profiling outcomes observed by dividing our pi-Profiling Perimeter P diameters D with . .

pi-Profiling Formula Facilitator ( f1 ) formally pPCFa .

being 16/pi . .

Square root of x formula number one (SOXf#1) within the numerical .

environment of our pi-Profiling Perimeter denoted P .

sqrt of x =~ {sqrt ( x * 31.8309886…%) } * 1.7724538…

Author: Kevin John Trinder .

Independent researcher .

Please note i am dyslexic and use of the periods is to keep me focused .

Began October 30th 2013. ( updated April 8, 2016 ) .

i have no affiliation with academia

Introduction .

We began this paper on October 30th 2013. .

Changes have been made every day or so as i try to find the words seeds of notion .

the numerical environment of our to communicate my observations made within and about .

Page ! of !18 25

the numerical environment of our p-Profiling Perimeter P using electronic spread sheets. . .

This paper is about my Number Theory research, Post January 2012. . .

My Number theory research Pre January 2012, dates back more than twenty years.

Number Theory research, Post January 2012. .

Please note i am dyslexic and use of the periods is to keep me focused .

i tend to visually capture simultaneously right-left-right to the centre .

some symbols and word letters .

√ [{( b, d, f, p, q, r and it is also difficult for me to write the letters f and r)}]√ .

are not readily visually recognisable to me, e.g. . .

There are many scientific symbols such as the radical sign and brackets that are .

not easily recognised by me. . .

As words and formulas get larger (more characters or variables) parts of them .

disappear on me, so forgive any frustration my presentation is causing you.

Change of denotation November 22nd, 2013 .

Because of an observed pi outcome for the square root of 1.125 .

Go to Web link: .

n.b. link removed at this time, reference for √1.125 is given above .

Known Numerical Facilitators (KF’s) .

Known Numerical Facilitator Ratios (KFR’s). .

pi-Profiling Constant Ratios Facilitators (pi-PCF’s)

pi-Profiling Formula Facilitators ( pPFf’s )

Abstract .

Known Numerical Facilitator Ratios (KF’s) .

for the square root of x formula number 1 ( SOXf#1 ) .

from the notion and origin of or for the square root of x ( SOX ) .

within the numerical environment of our perimeter ( P ) .

n.b. the X in SOXf’s formulas are positive numerical value in general, representing .

the diameter (D) on 4 i.e. D/4 of our NP, we denote and write D/4 as Di .

[ why Di and De?, in the real world Di is short for Diane and De is short for Diane Elizabeth ]

Page ! of !19 25

Denotation for pi-profiling observations when we assign a positive number in general .

to the diameter D of our pi-Profiling Perimeter P. . .

Our perimeter P is symbolised by ⊙ .

Our ⊙’s companion (c) P symbol is denoted k . .

Our ⊙’s area is denoted ⊙A or just write, A .

Our k’s area is denoted kAc or just write, Ac . .

Our ⊙’s radius is denoted ⊙R or just write, R .

Our k’s radius is denoted kRc or just write, 2017: Rc .

.

Our ⊙’s perimeter is denoted ⊙P or just write, 2017: P .

Our k’s perimeter is denoted kPp or just write, 2017: Pc . .

Our ⊙’s diameter (D) is denoted ⊙D or just write, 2017: D .

Our k’s diameter is denoted kDc or just write, Dc . .

Our ⊙’s diameter on 4, i.e. D/4, is denoted Di or ⊙ Di or just write, Di .

Our k’s diameter on 4, i.e. kDc /4 is denoted De or kDe or just write, De . .

Our ⊙’s perimeter increments are denoted ⊙Ps or just write, Psi .

Our k’s perimeter increments are denoted kPs or just write , Psic . .

Our ⊙’s companion Sphere is denoted and written, S .

Our k’s companion Sphere is denoted and written, Sc . .

Our ⊙’s companion Spheres surfaces area is denoted, Ssa .

Our k’s companion spheres surface area is denoted, Ssac . .

Our ⊙’s companion spheres volume is denoted, SV .

Our k’s companion spheres volume is denoted, SVc .

The sqrt of Di has a companion square root value (csv), denoted csqrtx .

Page ! of !20 25

The sqrt of Di (Di or D/4 may be considered to be any positive number x value, in general) .

and its csqrtx value, interact with x^2, the inverse of x and the known numerical .

constant Facilitator (KF) positive integer 1728. . .

For me it follows that for the many facets of geometry and companion values for them .

we may be to observe within and about the numerical environment of our

pi-Profiling Perimeter P many more Numerical Facilitating Constant Ratios Facilitators (NFCFs) .

which i have now denoted .

pi Profiling Constants Ratios Formula Facilitators ( pPFf’s ) . .

It is May 28th 2014 now April 7, 2016 and i have tried to find terminologies that are not to far from .

our daily workings with pi-Profiling Perimeters P when we assign a positive numerical value .

in general, as our diameter D. . .

These pPFf’s link our P ⊙ with many numerical outcomes of Geometry and their companion .

values very efficiently .

Authors note: In January 2016 we introduced the symbol for our csqrtx as wDi .

n.b. wDi stands for my notion of the companion square root of x and work-around for 1Pe2 . .

Denotation for pi-profiling observations when we assign a positive or negative .

number in general, as the number of wDi increments .

about our pi-Profiling Perimeter P. .

Our perimeter P when using wDi is symbolised by ⊙ .

Our ⊙’s companion P symbol is denoted k . .

Our ⊙’s area is denoted ⊙A or just write A .

Our k’s area is denoted kAc or just write Ac . .

Our ⊙’s radius is denoted ⊙R or just write, R .

Our k’s radius is denoted kRc or just write, Rc .

.

Our ⊙’s perimeter is denoted ⊙P or just write, P .

Our k’s perimeter is denoted kPp or just write, Pc . .

Page ! of !21 25

Our ⊙’s diameter is denoted ⊙D or just write, D .

Our k’s diameter is denoted kDc or just write, Dc

.

.

Our ⊙’s diameter on 4, i.e. D/4, is denoted Di or ⊙Di or just write, Di .

Our k’s diameter on 4, i.e. kDc /4 is denoted De or kDe or just write, De

.

.

Our ⊙’s perimeter increments are denoted ⊙Ps or just write, Psi .

Our k’s perimeter increments are denoted kPs or just write, Psic

.

. Our ⊙’s companion Sphere is denoted and written, S

. Our k’s companion Sphere is denoted and written, Sc

.

.

Our ⊙’s companion Spheres surfaces area is denoted and written, Ssa .

Our k’s companion Spheres surface area is denoted and written, Ssac

.

. Our ⊙’s companion Spheres volume is denoted and written, SV

. Our k’s companion Spheres volume is denoted and written, SVc

Authors note: October 26th, 2014. .

On October 26th 2014, i observed the pi-Profiling Formulas (pi-PF’s) for .

giving our pi-Profiling Perimeters its companion Ellipse its Surfaces area, denoted HESa and .

we observed the companion surface area to HESa denoted kHESA .

The pi-Profiling Formulas (pi-PF’s) for

giving our pi-Profiling Perimeters its companion Ellipsoid its volume denoted EDHV .

and observing the companion volume to EDHv denoted kEDHV .

was very special moment for me. .

Authors note October 30th 2014, my next priority: .

i am now looking for a pi-Profiling Formulas (pi-PCF’s) for our .

pi-Profiling Perimeters companion Ellipsoid’s Surface Area .

when and if found, to be denoted EDHSa .

either a yes or no result, will be an interesting outcome, i am thinking in the affirmative.

.

.

Page ! of !22 25

Known Numerical Facilitator Ratios (KF’s) for our SOXf#1 .

KF’s for SOXf#1 : Square root of x =~ {sqrt [(( x*(((1/pi)*100))%)]} * square root of pi

.

.

KF’s for SOXf#1: .

Square root of x =~ { sqrt ( x * 31.830988618379… %) } * 1.7724538509…

for x equals positive integer 19 .

sqrt of positive integer 19 =~ 4.35889894

1/ 19 * 31.830988618379 % =~ 6.047887837… .

2/ sqrt 6.047887837 =~ 2.45924538… .

3/ 2.45924538 * 1.7724538509… =~ 4.35889894…

. For the above SOXf#1 we see 31.830988618379…% is the

.

known numerical constant Facilitator pi-Profiling Formula Facilitator (pPFf) of or for (1/pi)*100 .

and .

1.7724538509… is the KCF pi-PCF of or for sqrt of pi. .

n.b. we also observe .

KF’s for SOXf#1 as : Square root of x =~ {sqrt [( x / pi )]} * sqrt of pi .

or as, for positive numerical values n in general: .

SOXf#1 : Square root of x =~ { sqrt [( x / n )] } * sqrt of n

. Variations of SOXf#1

.

SOXf#2: .

as at April 3rd, 2014. SOXf#2 is still being resolved, August 16, 2014. . .

March 27th, 2014: SOXf#3 .

being the sqrt x =~ { [sqrt of (x/2)] / sqrt 2 } .

n.b. SOXf#3 is a variation of SOXf#1

.

.

March 28th, 2014: SOXf#4 .

being the sqrt x =~ [sqrt{[(8/pi)^2]*x}] / [(8/pi)]

Page ! of !23 25

n.b. SOXf#4 is a variation of SOXf#1 .

SOXf#5 through SOXf#11 as at August 16th 2014. are still being resolved.

.

.

March 29th, 2014: SOXf#7 .

the sqrt {PNVIG} =~ sqrt{ ([PNVIG] / [pi^3]) } * [sqrt(pi^3)] .

where PNVIG, is a positive numerical value in general .

and is our diameter (D) on 4, (D/4)

.

.

n.b. SOXf#7, is a variation of SOXf#1 .

SOXf#12 through SOXf#31 have not been observed as at August 16th, 2014.

.

.

March 27th, 2014: SOXf#32: Trinder’s Cosmos Constant Pp#32 constant pi formula being: .

Pp#32 =~ [sqrt{[(8/pi)^2]*10}] / [(8/pi)] from

.

[ {[(8/pi)^2]*(40 pi)} / {sqrt of [(8/pi)^2]} ] / 32 Pp#32 constant pi formula is a variation of SOXf#1

.

.

May 22nd, 2014: SOXf#Cn .

SOXf#Cn: sqrt of x =~ {[sqrt (x/pi)]*2} / [{[(Cn)^2] * (4 pi)} / (10^18)]

.

where Cn is our Notional Speed of Light (Cn) value of 299,655,737.5766…

.

Cn =~ sqrt {[{(2*pi)/sqrt(pi^3)}*10^18] / (4*pi)} =~ 299,655,737.5766…

.

.

Known Numerical Facilitator Ratios (KF's) is a name i have given or denoted to many .

observed numerical outcomes, being a manipulation or extraction of pi when assigning .

a positive numerical value in general to diameter D .

and at times KF’s may be observed as pi-Profiling Formula Facilitators ( pPFf’s ) .

within and about the numerical environment of our pi-Profiling Perimeter P. .

Geometrical Mensuration aid Values given and passed down and improved along the way from .

ancient times are also observed with and about the numerical environment of our pi-Profiling Perimeter P

.

Page ! of !24 25

.

My research into the behaviour of numbers, searching for a mental image for the square root of x .

within and about the numerical environment of our pi-Profiling Perimeter P, began about twenty .

years ago and .

the numerical outcomes observed would not have been possible without computerised .

spreadsheets being available to us. .

n.b. You may use, copy or store these KF’s for our square root of formulas, there variations and .

pi-Profiling Formulas and these pi-Profiling Concepts, for educational purposes with .

attribution to me where possible. . . .

pi-Profiling Information . .

Author: Kevin John Trinder, began October 30, 2013. updated August 10th 2018. 7:18 AM.

Page ! of !25 25